Question

Help please please please

Answer 1

1.
`F_1(0,-√(35)),\ F_2(0,√(35)).`

2.
`F_1(0,-√(12)),\ F_2(0,√(12)).`

3.
`F_1(-√(5),0),\ F_2(√(5),0).`

Explanation:

The foci of ellipse have the coordinates
`F_1(-c,0),\ F_2(c,0),` where
`c=√(a^2-b^2)` if a>b and
`F_1(0,-c),\ F_2(0,c),` where
`c=√(b^2-a^2)` if b>a.

1.
`a=1,\\ \\b=6,\\ \\c=√(36-1)=√(35)`

and foci are on y-axis
`F_1(0,-√(35)),\ F_2(0,√(35)).`

2.
`a=2,\\ \\b=4,\\ \\c=√(16-4)=√(12)`

and foci are on y-axis
`F_1(0,-√(12)),\ F_2(0,√(12)).`

3.
`a=3,\\ \\b=2,\\ \\c=√(9-4)=√(5)`

and foci are on x-axis
`F_1(-√(5),0),\ F_2(√(5),0).`